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Scholkopf, B., Smola, A.J., Bach, F., et al. (2002) Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge.

has been cited by the following article:

• TITLE: Quasi-Monte Carlo Approximations for Exponentiated Quadratic Kernel in Latent Force Models

  AUTHORS: Qianli Di

  KEYWORDS: Latent Force Model, COVID-19, Quasi-Monte Carlo Approximations

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.10 No.4, October 13, 2022

  ABSTRACT: In this project, we consider obtaining Fourier features via more efficient sampling schemes to approximate the kernel in LFMs. A latent force model (LFM) is a Gaussian process whose covariance functions follow an Exponentiated Quadratic (EQ) form, and the solutions for the cross-covariance are expensive due to the computational complexity. To reduce the complexity of mathematical expressions, random Fourier features (RFF) are applied to approximate the EQ kernel. Usually, the random Fourier features are implemented with Monte Carlo sampling, but this project proposes replacing the Monte-Carlo method with the Quasi-Monte Carlo (QMC) method. The first-order and second-order models’ experiment results demonstrate the decrease in NLPD and NMSE, which revealed that the models with QMC approximation have better performance.